Question

Nine times the side of one square exceeds a perimeter of a second square by one metre and six times the area of the second square exceeds twenty nine times the area of the first by one square metre. Find the side of each square.

Answer 1

Hey dear,

● Answer-
s1 = 5
s2 = 11

● Explaintion-
# Given-
9s1 = p2 + 1
6A2 = 29A1 + 1

# Solution-
We have
9s1 = p2 + 1
9s1 = 4s2 + 1
s2 = (9s1-1)/4 ...(1)

Also,
6A2 = 29A1 + 1
6s2^2 = 29s1^2 + 1

Putting values,
6(9s1-1)^2/16 = 29s1^2 + 1
486s1^2 - 108s1 - 6 = 464s1^2 + 16
11s1^2 - 54s1 - 5 = 0 ...(2)

Solving (1) and (2),
s1 = 5
s2 = 11

Hope this is useful...

Answer 2

Side of square 1 = x = 5

Side of square 2 = y = 11

Refer to the images attached.

I've applied both methods, i.e., Factorization and Quadratic Formula.

Hope it helps!